A stochastic games framework for verification and control of discrete time stochastic hybrid systems |
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Authors: | Jerry Ding Maryam Kamgarpour Sean Summers Alessandro Abate John Lygeros Claire Tomlin |
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Affiliation: | 1. Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA;2. Automatic Control Laboratory, Department of Information Technology and Electrical Engineering, Swiss Federal Institute of Technology (ETH) Zürich, CH-8092 Zürich, Switzerland;3. Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK |
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Abstract: | We describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting. In particular, we consider finite horizon zero-sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space, and a rational adversary has the opposing objective. We derive an algorithm for computing the maximal probability of achieving the control objective, subject to the worst-case adversary behavior. From this algorithm, sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst-case disturbance strategies. These results are then specialized to the safety problem, in which the control objective is to remain within a safe set. We illustrate our modeling framework and computational approach using both a tutorial example with jump Markov dynamics and a practical application in the domain of air traffic management. |
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Keywords: | Hybrid systems Stochastic systems Dynamic games Controller synthesis Reachability |
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